Three men caught taking discarded food from bins outside an Iceland store will not now be prosecuted after an explosion of criticism over the decision to bring charges against them, including from the company's chief executive.

The Crown Prosecution Service said it would drop its case despite having previously said there was "significant public interest" in prosecuting the men. They were caught last year taking tomatoes, mushrooms, cheese and Mr Kipling cakes from the dustbins behind a branch of the high-street retailer.

Baljit Ubhey, the chief crown prosecutor for the CPS in London, said: "This case has been reviewed by a senior lawyer and it has been decided that a prosecution is not required in the public interest."

The Guardian revealed on Tuesday that Paul May, Jason Chan and William James had been charged under the 1824 Vagrancy Act, after being discovered in "an enclosed area, namely Iceland, for an unlawful purpose, namely stealing food".

The retailer took rapid steps to distance itself from the case, attempting to offset a damaging public relations storm as news of the prosecution triggered widespread criticism. Several online petitions were launched, calling on the CPS to reconsider its decision to prosecute.

May Chan and James, all residents of a squat in north London, were arrested on 25 October, just before midnight, after a member of the public called the police to report three men scaling a wall at the back of Iceland in Kentish Town. Police arrested the men as they left the area with a holdall and trolley containing food. The total value of the items taken from the bins allegedly amounted to £33.

May, 35, a freelance web designer, said he was relieved the case had been dropped. He said it was a ridiculous charge, and "crazy" to think that prosecution was in the public interest.

He said he had taken the food because he needed it to eat and did not consider that he had done anything illegal or dishonest in removing food destined for landfill from a skip.

"Did we have dishonest intent when we jumped into the yard at Iceland to retrieve what was in the bins? No, we didn't," he said. "A dishonest action would be wandering into a store and filling your pockets with what is on the shelves. We didn't do that."

May said he was not ashamed of recovering binned food, to share, cook and eat with his housemates.

"It doesn't feel like we are doing something criminal. We are taking food that they have thrown away so it can be eaten by people who appreciate it. I think it is more morally questionable that they are throwing away that much usable food than that people are diving in and recovering it. In some ways I am proud of what we do."

Walker said his initial reaction to news of the prosecution had been "one of total bemusement". Writing in the Guardian, he said: "Our store had not called the police, let alone asked for those concerned to be prosecuted. Waste food in our bins that cannot be sold is clearly of minimal value to us."

He added: "We acted as soon as we could to ask the police and CPS to drop the case."

The case has prompted new focus on the phenomenon of "skipping" – taking discarded supermarket waste to cook and eat – and reopened the debate over how much supermarket food is still discarded.

But although some supermarkets here are beginning to offer their unused stock to food banks, May says the quantity still found discarded in bins suggests there is much more that could be used constructively.

Explaining the decision to drop the case, Ubhey said: "In reconsidering this case, we have had particular regard to the seriousness of the alleged offence and the level of harm done. Both of these factors weigh against a prosecution. Additionally, further representations received today from Iceland Foods have affected our assessment of the public interest in prosecuting."

"We hope this demonstrates our willingness to review decisions and take appropriate and swift action when necessary. The Crown Prosecution Service is committed to bringing the right charges to court when – and only when – it is proper to do so."

The case was launched as attitudes towards excessive supermarket waste begin to harden. In the US, entrepreneurs are working on new models for recycling unsold produce.

May, who has regularly taken food from skips, argued that he had the right to take food which was being thrown away. "More and more people are using food banks than ever before but supermarkets are throwing away huge amounts of food, which will end up in landfill," he said. "If supermarkets were giving as much as they could away, then their bins would be empty, or full of cardboard boxes and broken yoghurt pots – but they're not. You'd be amazed at what you find."

He and other residents at the squat regularly find large quantities of frozen chicken breasts. Last week, they had quail. Most of the food May collects when he goes skipping has crossed the marked sell-by date, but is still edible.

The residents of the squat have a kitty where people contribute to basic necessities such as teabags and milk, but the bulk of what residents eat comes from skips, May said.

May says he is squatting because he cannot afford to rent in London and the alternative would be to move out of the city, making it hard to see his six-year-old son. Removing food from skips allows him to eat more healthily than he would if he was buying food on a low income, he claims. "If I relied on the little I have every day, I would eat very badly."